Method and apparatus for single burst equalization of single carrier signals in broadband wireless access systems

ABSTRACT

A receiver implementing a single carrier single burst equalization (SC-SBE) method is capable of achieving near optimal reception of individual single carrier RF bursts by making an accurate estimate of the burst&#39;s propagation channel impulse response (CIR). The SC-SBE method uses a CIR based coefficient computation process to obtain filter coefficients for a minimum mean square error decision feedback equalizer (MMSE-DFE). The MMSE-DFE filter computation process computes a sufficiently large number of coefficients for the DFE filters, i.e., the feed forward filter (FFF) and feedback filter (FBF), so that each filter spans the maximum anticipated length of the CIR. In order to implement the filters efficiently, a coefficient selection process eliminates less significant computed FFF and FBF coefficients. The resulting FFF and FBF are sparse filters in that most of the taps in the filter delay lines do not have a filter coefficient.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.12/157,738, filed on Jun. 12, 2008, which in turn is a continuation ofU.S. patent application Ser. No. 10/796,596, filed on Mar. 9, 2004, nowissued U.S. Pat. No. 7,388,910, issued on Jun. 17, 2008, which claimspriority to a U.S. Provisional Application No. 60/453,162, filed on Mar.10, 2003, entitled METHOD AND APPARATUS FOR SINGLE BURST EQUALIZATION OFSINGLE CARRIER SIGNALS IN BROADBAND WIRELESS ACCESS SYSTEMS, the contentof each of which is incorporated herein by reference.

BACKGROUND OF THE DISCLOSURE

The development of wireless metropolitan area networks (WMAN's) andwireless local area networks (WLAN's) for broadband wireless access(BWA) to voice and data telecommunication services is an area ofconsiderable economic and technological interest. The WMAN systemstypically employ a point-to-multipoint topology for a cost effectivesystem deployment. For example, proposed WMAN systems operating in the 2to 6 GHz radio frequency (RF) range consist of base station cell towersites with 3 to 6 antenna/transceiver sectors, with capacity goals of 40to 80 Megabits per sector, and with coverage goals of 5 to 15 kilometercell radius. Example WLAN systems include installations at areas bothinside and outside of residences or businesses and public areas such astrains, train stations, airports or stadiums. These WMAN and WLANsystems can also be integrated to form a wide area network (WAN) thatcan be national or even global in coverage. WMAN systems are primarilydiscussed because they are technically the most challenging. However,the invention may also be used in broadband wireless access systems ingeneral.

The primary problem in broadband wireless telecommunication is theconsiderable variation in the quality of the RF reception. The RFreception varies due to the type of terrain, due to the presence ofobstacles between the base station and the subscriber station (SS), anddue to the fairly high probability of receiving the same transmission bymeans of multiple RF propagation paths. The latter problem is referredto as “multipath” and the above set of reception problems is oftencollectively, and loosely, referred to as the non-line-of-sight (NLOS)reception problem. When the SS is moving, there is the additionalproblem of Doppler induced channel variability. A robust NLOS BWA systemfor fixed or mobile subscribers is a technical challenge.

The WMAN systems of interest typically have RF channels that are thecomposite of multiple radio propagation paths over large distances. Aconsequence of these multipath propagation channels is that the receivedradio signal waveforms are distorted relative to the originaltransmitted radio signal waveforms. Prior art high data rate WMANsignaling technologies that are intended to mitigate the multipathperformance degradations are orthogonal frequency division multiplexing(OFDM) and single carrier with frequency domain equalization (SC-FDE).

FIGS. 1 and 2 are diagrams of known OFDM and SC-FDE methods oftransmitting and receiving signals with digital data modulations throughdispersive propagation channels that impose some degree of multipathsignal distortions. These diagrams emphasize the method specific signalprocessing elements and illustrate their dependence on FFT blockprocessing.

FIG. 1 shows a block diagram illustrating certain processes performed bya system implementing the OFDM method. An inverse fast Fourier transform(inverse FFT) 110 transforms the data (symbols) 108 to be transmitted.Cyclic prefix insertion process 112 creates a serial output block withends that are circular in content. These processes occur within OFDMtransmitter 114. The transmitter output 115 passes through a propagationchannel 116 to become input 117 to OFDM receiver 118. The methodspecific processes the OFDM receiver include a forward fast Fouriertransform (FFT) process 120 that creates intermediate data symbols thathave been distorted by the propagation channel, a process 122 to invertthe channel and a process 124 to detect the original symbols, i.e., toprovide the received data output 126. The OFDM symbol detection process124 may, for example, include Viterbi decoding, symbol de-interleaving,and Reed-Solomon forward error detection/correction (FEC). The specificdetection process 124 depends on the coding/interleaving that wasapplied to the transmitted data symbols 108.

FIG. 2 shows a block diagram illustrating certain processes performed bya system implementing an SC-FDE method. The data symbols to betransmitted 128 are input to a preamble and cyclic prefix insertionprocess 130. The preamble sequence has good correlation properties tosupport channel estimation and the cyclic prefix insertion createscircular output blocks to simplify receiver FFT operations. Theseprocesses occur within SC-FDE transmitter 132. The transmitter output133 passes through a propagation channel 134 to become input 135 toSC-FDE receiver 136. The method specific processes in SC-FDE receiver136 include a forward FFT 138 process to transform the signal into thefrequency domain, a frequency domain filter to invert the channel 140,an inverse FFT 142 to restore the signal to the time domain, and symboldetection 144 that provides the received data output 146. The SC-FDEsymbol detection process 144 may include a non-linear decision feedbackequalizer (DFE) in addition to decoding and de-interleaving operations.As in the OFDM method, the detection process 144 may, for example,include Viterbi decoding, de-interleaving, and a Reed-Solomon FEC, orfunctionally similar operations, depending on the coding/interleavingthat was applied to the transmitted data symbols 128.

Operationally, the OFDM and SC-FDE systems differ mainly in theplacement of the inverse FFT. In the OFDM method the inverse FFT is atthe transmitter to code the data into the sub-carriers. In the SC-FDEmethod the inverse FFT is at the receiver to get the equalized signalback into the time domain for symbol detection. Although FIG. 2 showsthe SC-FDE signal to have a cyclic prefix insertion 130, this isactually an option for SC-FDE that trades useable bandwidth for aslightly decreased number of receiver computations and a potentialperformance improvement. In the OFDM method, the cyclic prefix insertion112 and the associated loss of useable bandwidth are mandatory.

For high data rate single carrier (SC) systems, WMAN multipath RFchannel distorts the signal by mixing data symbols that were originallyseparated in time by anywhere from a few symbols to a few hundreds ofsymbols. This symbol mixing is referred to as inter-symbol interference(ISI) and makes the SC wireless link useless unless equalization isperformed. It is generally agreed that traditional time domain adaptiveequalization techniques are impractical to solve this problem since thecomputations per bit are proportional to the ISI span, which in the WMANchannels of interest can be hundreds of symbols. However, the FFT can beused to provide efficient frequency domain equalization for singlecarrier signaling. This is the basis of the single carrier frequencydomain equalization (SC-FDE) method discussed above. SC-FDE is known towork well in terms of multipath mitigation and is practical in terms oftransceiver computations per bit. A modem SC-FDE method is described byDavid Falconer, Lek Ariyavisitakul, Anader Benyamin-Seeyar and BrianEidson in “Frequency Domain Equalization for Single-Carrier BroadbandWireless Systems”, IEEE Communications Magazine, Vol. 40, No. 4, April2002.

For high data rate OFDM systems, WMAN multipath RF channels often resultin severe spectral nulls. These spectral nulls make the OFDM wirelesslink useless unless interleaving and coding are performed. Coherent OFDMalso requires equalization. However, OFDM with interleaving, coding, andequalization is known to work well in terms of maintaining a WMAN linkin the presence of multipath and is equivalent to SC-FDE in terms oftransceiver computations per bit. A critical comparison of the OFDM andSC-FDE techniques is given by Hikmet Sari, Georges Karam and IsabelleJeanclaude in “Transmission Techniques for Digital Terrestrial TVBroadcasting”, IEEE Communications Magazine, February 1995.

SUMMARY OF THE DISCLOSURE

The invention allows for use of time domain equalization in singlecarrier broadband wireless systems, thereby overcoming one or moreproblems associated with using traditional time domain equalizationtechniques and avoiding the disadvantages of OFDM and SC-FDE systems.

An example of one use of a preferred embodiment of the invention is areceiver implementing a single carrier single burst equalization(SC-SBE) method. Such a receiver is capable of achieving near optimalreception of individual single carrier RF bursts. The receiver makes anestimate of the burst's propagation channel impulse response (CIR) andthen uses a CIR-based coefficient computation process to obtain filtercoefficients for a time domain equalization process. A subset comprisingthe most significant coefficients is selected for filters in theequalization process allowing more efficient implementation of thefilters in the time domain.

For example, if a time a minimum mean square error decision feedbackequalizer (MMSE-DFE) used a MMSE-DFE filter computation process computesa sufficiently large number of coefficients for the DFE filters, i.e.,the feed forward filter (FFF) and feedback filter (FBF), so that eachfilter spans the maximum anticipated length of the CIR. For NLOS WMANsystems, this results in hundreds of computed coefficients for both theFFF and the FBF. In order to implement the filters efficiently, acoefficient selection process eliminates less significant computed FFFand FBF coefficients. The resulting FFF and FBF are “sparse” filters inthat the sense that most of the taps in the filter delay lines do nothave a filter coefficient. This allows the filters to be efficientlyimplemented in the time domain.

The availability of time domain, sparse equalization filters avoidproblems associated with the prior art OFDM and SC-FDE methods which useblock processing FFT procedures. These problems include a large blockgranularity that limits bandwidth efficiency. In contrast, the SC-SBEmethod allows the bandwidth efficiency to be maximized. The coefficientselection process improves the radio telecommunication link'sperformance for the majority of WMAN propagation channels. In theremaining WMAN channels the coefficient selection procedures assure thatany performance degradation will be insignificant.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of the transmitter and receiver implementing aprior art OFDM method.

FIG. 2 is a block diagram of a transmitter and receiver that implement aprior art SC-FDE method.

FIG. 3 is a block diagram of a transmitter and receiver implementing aSC-SBE method with a coefficient selection process and sparse filterDFE.

FIG. 4 is a block diagram of a transmitter and receiver that illustratesthe SC-SBE operations relative to other operations in a single carrierreceiver.

FIG. 5 is a block diagram of an SC-SBE processor.

FIG. 6 is a block diagram illustrating a DFE performance basedcoefficient selection process with an exhaustive search.

FIG. 7 is a block diagram illustrating a DFE performance basedcoefficient selection process with amplitude based pre-selection.

FIG. 8 is a block diagram illustrating an amplitude threshold basedcoefficient selection process.

DETAILED DESCRIPTION OF THE INVENTION

A significant problem is created by both the OFDM and SC-FDE methods dueto their reliance on the large block FFT operation. The problem, notrecognized, is that the large block FFT operation restricts theefficiency of time division duplexing (TDD) and time division multipleaccess (TDMA) techniques. Modern TDD/TDMA techniques provide theopportunity for efficient use of a single RF channel for both downlinkand uplink burst communication. For example, adaptive TDD/TDMAtechniques, are defined in the IEEE Standard 802.16.TM.-2001. In theadaptive TDD technique the position in time of the border separating aTDD frame's downlink and uplink traffic is adapted to best suit therelative amount of downlink and uplink traffic. It is well known thatwhen properly implemented adaptive TDD is more spectrally efficient thanthe older frequency domain duplexing (FDD) technique which simply uses 2RF channels, one for downlink and one for uplink. Proper utilization ofTDD/TDMA techniques, however, requires flexibility with respect to theallowed (allocated) burst durations since the burst durations that aredesired depend on the variable size of the data to be transferred.

For WMAN systems, the OFDM and SC-FDE signaling techniques use an FFTwhose size is typically in the 256 to 2048 sample point range. Theproblem is that the block FFT operations impose a large granularity onthe TDD bandwidth allocation scheme that results in bandwidthinefficiency. The block restricted bandwidth allocation granularity isequivalent to the FFT size, in the range of 256 to 2048, or so,equivalent SC symbol time slots. This large TDD bandwidth allocationgranularity significantly decreases the efficiency of a TDD/TDMA BWAsystem. Another problem with the OFDM and SC-FDE methods that results inbandwidth inefficiency is the periodic insertion of a cyclic prefix—thisdirectly turns valuable bandwidth into overhead.

In contrast, methods and apparatus for single burst equalization ofsingle carrier RF communications signals (SC-SBE), described inconnection with FIGS. 3-7, do not require FFT operations or cyclicprefixes and provides greater flexibility in TDD bandwidth allocation,providing an allocation granularity/resolution of one single carriersymbol time slot. This allows the time-frequency bandwidth efficiency tobe optimized in a SC-SBE based TDD/TDMA BWA system. The SC-SBE methodtakes advantage of a coefficient selection process and a DFE that usestime domain sparse filters.

Note that the SC-SBE method and apparatus, described below in connectionwith FIGS. 3-7, has implementations at the system level of BWA systems,e.g., WLAN, WMAN and WAN systems, in components that make up the BWAsystems, e.g., base station and subscriber station receivers, and in thecircuits that make up the receiver or transceiver components. Unlessotherwise represented, circuitry for performing the functions orprocesses referenced below may be implemented as hardware, software, ora combination of hardware and software. Implementation examples includesoftware executing on a digital signal processor (DSP) or a generalpurpose computer, as well as logic elements executing in a fieldprogrammable gate array (FPGA) or an application specific integratedcircuit (ASIC). Discrete functional blocks in the figures do not implydiscrete hardware components.

FIGS. 3, 4 and 5 illustrate SC-SBE concepts with reference to functionalblock schematic diagrams of example embodiments of transmitters andreceivers. FIG. 3 is a block diagram of an example of a SC transmitterand SC-SBE receiver that facilitates a comparison with the OFDM andSC-FDE methods diagrammed in FIGS. 1 and 2. FIG. 4 is a block diagram ofa SC-SBE receiver that illustrates the relation of the SC-SBE operationsto other receiver operations, in particular the SC-SBE functions as apre-processor to standard detection circuitry such as a Viterbi decoder.FIG. 5 is an example of a SC-SBE DFE with sparse, time domain filters.

Referring to FIG. 3, the data symbols to be transmitted 158 bytransmitter 162 are input to preamble insertion circuitry 160 thatinserts a preamble symbol sequence having good correlation properties tofacilitate an estimation of the propagation channel impulse response.The transmitter output 163 is an RF signal burst that passes through apropagation channel 164 to become the input 165 to receiver 166.

In receiver 166, multipath channel equalization is accomplished with asparse filter DFE 168, described below. The input signal is delayed by apredetermined amount by delay circuit 170. The delay is to allow timefor the following to take place. A CIR estimate 173 is computed byprocess 172. Estimates 175 of signal power and noise power are computedby process 178. The signal power estimate is used to set an input gain176 for the sparse filter DFE 168. The MMSE-DFE filter coefficients 179are computed by process 178 based on the CIR estimate 173 and the noisepower estimate 175. The filter coefficient subset 183 is selected byprocess 182 using methods described below. The selected filtercoefficient subset 183 allows a high performance DFE 168 based onefficient time domain sparse filters.

The DFE 168 provides channel equalized data 191 to symbol detectionprocess circuitry 196 that performs symbol decoding and de-interleavingoperations. The operations of symbol detection 196 are the inverse ofthe coding/interleaving operations applied to the transmitted datasymbols 158. Symbol detection 196 provides the received data output 197that is of interest to the media access control (MAC) layer of the BWAsystem's base stations or subscriber stations.

It is preferred that the processing delay 170 is less than the minimalRF signal burst duration which is on the order of 50 microseconds. Thisrequirement insures that the receiver is capable of maintaining realtime throughput at the TDD frame time scale which is on the order of 2to 4 milliseconds.

FIG. 4 is a block schematic diagrams that illustrates the SC-SBEprocessing circuitry relative to other operations in one exemplaryembodiment of a receiver. In this example an SC-SBE circuit 198 isinserted between a conventional SC receiver front-end/timing recoverycircuit 200 and a conventional symbol detection circuit 196.

Referring to FIG. 4, in the SC receiver front-end processing circuitry200, an RF signal is acquired by antenna 201 and processed by analogamplification, filtering and frequency down conversion 202 to provide amuch lower frequency analog baseband or pass-band signal 203 that can beconverted into digital samples by sampling circuitry 204 for subsequentdigital signal processing. Pulse shape filter 206 provides signalmatched filtering that eliminates out of band noise and provides asignal 207 suitable for feed-forward timing recovery circuitry 208.Timing recovery in the SC receiver front-end processor 200 is desirablesince it allows subsequent processing to be performed more efficientlyusing only one digitized sample per symbol. To achieve the timingrecovery, the flow of the digitized burst signal is delayed by apredetermined amount by delay circuit 210. The delay is to allow timefor symbol timing recovery circuitry 212 to compute the timing offsetestimate 213. The timing estimate 213 controls interpolation circuitry214 which outputs near optimally sampled data 215 to the SC-SBE circuit198.

As illustrated in FIG. 4, SC-SBE circuitry 198 can function as apre-processor to a traditional symbol detection process or circuitry196. For a more explicit example, symbol detection could be based on thetransmit coding specified by the IEEE Standard 802.16a.TM.-2003. In thiscase the symbol detection circuitry 196 would be a Viterbi decoder, ade-interleaver and a Reed-Solomon FEC, followed by a de-randomizer torecover the transmitted data of interest. The SC-SBE circuitry 198 doesnot depend on, nor require knowledge of, the type of symbol detectioncircuitry 196 that follows it. The detection circuitry 196 outputs thereceived data 197 that is sent to a MAC layer, not shown.

Referring to FIG. 4, the CIR estimation process 172 in the SC-SBEcircuit 198 can, for example, be performed with known non-parametriccross-correlation techniques in which the received preamble data iscross-correlated with the transmitted preamble data. Example preamblesthat are well suited for a cross-correlation based CIR estimation arethe so called constant amplitude zero autocorrelation (CAZAC) sequences.The IEEE Standard 802.16a.TM.-2003 specifies a CAZAC sequence for thispurpose.

The signal (S) and noise (N) power estimation process 174 can bedesigned based on a variety of known methods. For example, a preamblecomposed of multiple CAZAC sequences can be Fourier transformed over atime interval spanning two contiguous sequences. The power at evenharmonics of the total period is an estimate of the signal plus noise(S+N) power, whereas the power at odd harmonics is an estimate of thenoise power, N 175. The signal only power can then be estimated bysubtraction. The input gain 176 that is required by the sparse filterDFE 168 can be computed as the ratio of the desired signal level to thesquare root of the estimated signal power, S.

The CIR estimate 173 and the noise power estimate 175 are input to theMMSE-DFE filter coefficient computation process 178. Three alternativefast methods are known that can compute the filter coefficients 179 foran MMSE DFE from a CIR estimate and a noise power estimate. Thesepublished, computationally efficient MMSE-DFE coefficient computationprocedures are: Naofal Al-Dhahir and John M. Cioffi, “Fast Computationof Channel-Estimate Based Equalizers in Packet Data Transmissions”, IEEETransactions on Signal Processing, pp. 2462-2473, 11, 43 (November1995); Bin Yang, “An Improved Fast Algorithm for Computing the MMSEDecision-Feedback Equalizer”, Int. J. Electronic Communications (AEU),Vol. 53, No. 6, pp. 339-345 (1999); and N. R. Yousef and R. Merched,“Fast Computation of Decision Feedback Equalizer Coefficients”, U.S.Patent Application 2003/0081668 (May 1, 2003). Each of these coefficientcomputation procedures can be used to efficiently compute the largenumber, e.g., hundreds, of filter coefficients 179 that define the longtime span filters required by the DFE for WMAN systems.

The reason channel equalization filters with long time spans arerequired is, that in order to be effective, the filters must span themaximum variability in the propagation delay in the multipath channel.This maximum variability is generally quantified by the ‘delay spread’parameter. In order to characterize a multipath channel, it's CIR mustbe measured for delays somewhat larger than the delay spread. Forexample, in some WMAN systems, the multipath delay spread can exceed 10microseconds and, typically, a single carrier signal having a 20 MHzbandwidth can be modulated with 16 million symbols per second. If theDFE filters for this SC system support the conventional minimum of onecoefficient per symbol, this equates to greater than 160 coefficientsper filter. It is straightforward to estimate the CIR over a 10 or moremicrosecond time span, for example using the above mentioned CAZACcross-correlation technique. Furthermore, the above mentioned threealternative fast coefficient procedures provide means of computing thecoefficients 179. However, to directly implement filters with such alarge number of filter coefficients in the time domain would require aninordinately large amount of computation.

Indeed, this excessive time domain computation requirement was themotivation for the known SC-FDE method diagrammed in FIG. 2. However, asmentioned earlier, block FFT and cyclic prefix operations of the SC-FDEmethod create the problem of inefficient TDD/TDMA bandwidth utilization.The SC-SBE method and apparatus solve the computation problem byselecting a subset of the coefficients for a time domain filter. Thistime domain filter with sparsely populated coefficients (or “sparse”filter) provides approximation of the outputs of the time domain filterwhen all the calculated coefficients are used.

Thus, the coefficient selection process simplifies the DFE filters andimproves receiver performance. Furthermore, a sparse time domain filterDFE allows efficient TDD/TDMA bandwidth utilization. The coefficientselection process 182 examines the large number of computed MMSE-DFEcoefficients 179 to identify a much smaller subset of coefficients 183to be used by the DFE filters. The sparse, time domain filters of DFE168 efficiently implement these coefficients, avoiding the need for FFTfilter techniques that result in TDD/TDMA inefficiency.

FIG. 5 shows, in more detail, a schematic block diagram of an exampleSC-SBE processing unit 198 in order to illustrate the sparse, timedomain filter DFE circuit 168. Two outputs are shown from thecoefficient computation process 178: a complete set of feed forwardfilter (FFF) coefficients 180 and a complete set of feedback filter(FBF) coefficients 181. The ‘complete set of coefficients’ refers to theMMSE-DFE coefficient computation 178 providing the number ofcoefficients required to span the maximum time lag of the CIR estimate173, which, given the above 20 MHz bandwidth WMAN system example, couldresult in 160 or more FFF and FBF coefficients, each. The coefficientselection process 182 inputs the complete set of coefficients, 180 and181, and outputs a considerably smaller number of selected coefficients,184 and 185, for use in defining a sparse FFF 186 and a sparse FBF 188,respectively.

The sparse FFF 186 and the sparse FBF 188 preferably have delay linesequal in length to the number of coefficients in the complete sets, 180and 181, say greater than 160 each. However, the number of non-zerocoefficients in the sparse filters 186 and 188 are determined by theconsiderably smaller number of selected coefficients, 184 and 185, forexample, 16 each. The delayed received signal 171 is input to amultiplier circuit 194 having input gain 176 as the multipliercoefficient. This creates a signal amplitude scaled input 195 to thesparse FFF 186. The amplitude scaling matches the amplitude of thesignal component input to the FFF with the amplitude of the symboldecisions 193 that are input to the FBF 188. This allows the sparse FFFoutput 187 and the sparse FBF output 189 to be directly input tosummation circuit 190 to form the MMSE-DFE output 191, the channelequalized signal that is input to the subsequent symbol detectionprocess (not shown). The MMSE-DFE output 191 is also input to symboldecision circuitry 192 that provides the symbol decisions 193 that arein turn input to the sparse FBF 188.

As drawn in FIG. 5, the sparse FFF and FBF filters, 186 and 188, and thenonlinear symbol decision circuitry 192 constitute an example of a harddecision-decision feedback equalizer (H-DFE) structure. The H-DFE iswell known and has been extensively analyzed. Alternative decisionfeedback equalizer (DFE) structures exist that can readily takeadvantage of the coefficient selection and sparse time domain filterelements of the SC-SBE method by simply substituting the sparsecoefficient FFF and FBF filters defined above for the full coefficientFFF and FBF filters of the alternative DFE structure. An example of analternative DFE structure is the soft decision/delayed decisionintegration of the DFE and Viterbi decoder, referred to as the S/D-DFEand developed in S. Lek Ariyavisitakul, and Ye Li, “Joint Coding andDecision Feedback Equalization for Broadband Wireless Channels”, IEEE J.on Selected Areas in Communications, Vol. 16, No. 9, December, 1998.They indicate the S/D-DFE provides an approximate 3 dB performanceimprovement over the H-DFE. The performance advantage of the S/D-DFEstructure over the H-DFE structure can be expected to be retained whenthese SC-SBE methods and apparatus are applied to both structures.

The coefficient selection process 182 is a pruning of the complete setof coefficients that are output from the MMSE-DFE coefficientcomputation process 178. The coefficient selection process providesthree major benefits: the ability to perform computationally efficienttime domain equalization of channels having large multipath delayspreads; the ability to implement arbitrary TDD/TDMA bandwidthallocations using the minimal allocation granularity of one singlecarrier symbol; and improved overall receiver performance by avoidingthe use of FFF and FBF coefficients which decrease the performance. Thefirst benefit is based on the fact that sparse time domain filters canbe used to efficiently implement the reduced set of selected filtercoefficients, the number of selected filter coefficients probably needsto be less than 32. The second benefit is based on the fact that timedomain filters, in general, allow arbitrary TDD/TDMA bandwidthallocations with the minimal granularity, e.g., one single carrier (SC)symbol. As discussed above, in contrast to the block processingfrequency domain filtering techniques, standard time domain filteringdoes not impose block restraints on the TDD/TDMA allocation granularity,i.e., there is no additional computation cost for arbitrary start/stopallocations into a TDD time frame. The third benefit is improved overallreceiver performance, in terms of the nature of the typical CIR of aWMAN system and the coefficient selection process.

That the symbol error rate versus signal to noise ratio (SER versus SNR)performance can be improved with fewer taps is evident from the trivialexample of the ideal additive white Gaussian noise (AWGN) channel. TheDFE filter configuration that achieves the optimum performance for anAWGN channel is known to be equivalent to an all-pass filter. For theDFE to be equivalent to an all-pass filter requires that the tapselection algorithm select one FFF tap and zero FBF taps.

That the performance is typically improved is evident in the nature ofthe WMAN RF propagation CIR. An optimally sampled CIR typically has afew clusters of coefficients with each cluster consisting of only a fewsignificant coefficients. This sparsely clustered feature of a WMANpropagation channel CIR is due to the reflections near either thetransmit or receive antennas being convolved with reflections far fromeither antenna. The desired FFF and FBF filters mimic this sparselyclustered feature of the WMAN CIR. Setting maximums of 16 FFF and 16 FBFcoefficients is a conservative design for such channels. However, themaximum allowed number of coefficients is not critical and can be leftup to the implementation design engineer based on detailed engineeringdesign considerations. For example, extensive computer simulations withaccepted models for WMAN channels indicate that acceptable performanceis obtained with the maximum number of allowed coefficients set anywherebetween 8 and 32.

This leaves the relatively rare cases where, in order to obtain the bestDFE receiver performance, the WMAN CIR demands more than the allowedmaximum of N_sparse=16 or so coefficients each in the FFF and FBFfilters. Fortunately, since the example coefficient selection processesdiscussed below select the most significant coefficients, theperformance degradation in these cases will be slight. The slightlydiminished DFE performance associated with having only the N_sparse mostimportant coefficients is a good trade for what the coefficientselection process provides: efficient time domain equalization for NLOSWMAN channels with very large delay spreads and the bandwidth efficiencyassociated with arbitrary TDD allocations.

For example, consider an SC-SBE processor that estimates the CIR andcomputes the MMSE-DFE coefficients based on a received preamble composedof a 256 symbol length Frank CAZAC as defined in the IEEE Standard802.16a.TM.-2003. In this example, the MMSE-DFE coefficient computation188 outputs NF=256 computed FFF coefficients 180 and NB=255 computed FBFcoefficients 181. The coefficient selection procedure 182 inputs thecomplete set of computed coefficients and outputs, in this example atmost 16 or so most significant FFF coefficients 184 and at most 16 or somost significant FBF coefficients 185. With these selected coefficients,the sparse time domain FFF and FBF filters, 186 and 188, efficientlyspan a delay spread of 512 symbols while retaining a TDD/TDMA allocationgranularity of an individual symbol.

FIG. 6 illustrates a schematic block diagram of one example embodimentof the coefficient selection process 182. In this embodiment, thecoefficients are selected jointly for the FFF and FBF filters based onthe minimization of a DFE performance cost function. The received (RX)signal from timing recovery circuitry 215 is stored in an RX signalbuffer 300. The complete set of computed FFF and FBF coefficients, 180and 181, are stored in a computed coefficient buffer 302. Portions ofthe RX signal that contain known data 301 and a test FFF and FBFcoefficient subset 303 are input to a sparse filter DFE computationcircuit 304 that provides the DFE output 305 for input to a costfunction computation circuit 306. An example of a DFE performance costfunction is the averaged error vector magnitude (EVM) that can becomputed as the standard error of the DFE output relative to the knowndata. The DFE performance cost 307 is input to a minimization process310 that identifies the coefficient selection that minimizes the costsubject to the constraints that the number of FFF coefficients cannotexceed N_FFF 308 and the number of FBF coefficients cannot exceed N_FBF309. The minimization process 310 can be thought of as performing anon-linear parameter estimation where the parameters being estimated arethe addresses defining the coefficient subset, e.g., the test selection311, that minimizes the DFE performance cost 307. The results of thecost minimization coefficient selection, i.e., the sparse coefficientvectors, 184 and 185, are output to the sparse FFF and FBF filters, 186and 188, respectively.

A potential problem with the above embodiment of the coefficientselection process 182, as illustrated in FIG. 6, is that it isexhaustive in its search and may, consequently, require excessive timeand computation. FIG. 7 illustrates a schematic block diagram of amodification of the DFE cost minimization based coefficient selectionprocess that will reduce the search time and the associated computation.In this example embodiment, a pre-selection of the computed coefficientsto be searched is performed based on the coefficient amplitude. Thepre-selection consists of examining the computed FFF and FBFcoefficients, 180 and 181, to perform a selection 312 of the N_FFFlargest amplitude FFF coefficients 313 and a selection 314 of the N_FBFlargest amplitude FBF coefficients 315. The N_FFF largest FFFcoefficients 313 and the N_FBF largest FBF coefficients 315 are storedin a coefficient buffer 302 that defines the coefficient search spacefor the minimization process 310. This pre-selection based on amplitudecan be expected to have little effect on the DFE coefficient selection,i.e., the sparse coefficient vectors, 184 and 185, since the exclusionof small amplitude filter coefficients generally have little effect onthe filter output.

FIG. 8 illustrates a schematic block diagram of a third exampleembodiment of the coefficient selection process 182. This embodimentrequires neither the above iterative DFE performance cost minimizationprocedures nor any input of the received signal. In this embodiment thecoefficients are selected based on the computed coefficient's amplitudesatisfying two conditions: it is one of the N_FFF or N_FBF largestamplitude coefficients of the computed FFF or FBF coefficients,respectively; and it is bigger than K*.sigma..sub.F or K*.sigma..sub.B,where .sigma..sub.F or .sigma..sub.B are the standard deviations of theNF-N_FFF smallest amplitude computed FFF coefficients or NB-N_FBFsmallest amplitude computed FBF coefficients, respectively. Thresholdparameter input 331, represented by the variable K, that providesprotection against coefficient computation noise. NF and NB are thenumber of computed FFF and FBF coefficients, 180 and 181, respectively.N_FFF and N_FBF, 308 and 309, are the maximum number of non-zero FFF andFBF coefficients, 184 and 185, respectively, to be selected.

As illustrated in FIG. 8, the computed FFF coefficients 180 are sortedby amplitude sorting circuitry 316 into the N_FFF largest coefficients317 and the NF-N_FFF smallest coefficients 318. Similarly, the computedFBF coefficients 181 are sorted by amplitude sorting circuitry 320 intothe N_FBF largest coefficients 321 and the NB-N_FBF smallestcoefficients 322. The sets of smallest coefficients, 318 and 322, areinput to standard deviation circuitry, 324 and 326, that output thestandard deviations, .sigma..sub.F 325 and .sigma..sub.B 327. Thethreshold comparison circuitry 328 selects the non-zero sparse filterFFF coefficients 184 as the subset of the N_FFF largest computed FFFcoefficients 317 that are also greater than K*.sigma..sub.F. Similarly,the threshold comparison circuitry 330 selects the non-zero sparsefilter FBF coefficients 185 as the subset of the N_FBF largest computedFBF coefficients 321 that are also greater than K*.sigma..sub.B.

Comparing the above three example embodiments of the coefficientselection process 182, that are diagrammed in FIGS. 6, 7 and 8, thefollowing observations can be made. All three embodiments input thecomplete set of computed coefficients, 180 and 181, from the MMSE-DFEcoefficient computation process 178 and output the selected filtercoefficients, 184 and 185, that contain at most N_FFF and N_FBF non-zerocoefficients, respectively. The embodiments diagrammed in FIGS. 6 and 7require input of the RX signal and perform an iterative non-linear costminimization to achieve the coefficient selection. The embodimentdiagrammed in FIG. 7 performs a pre-selection based on the coefficientamplitude to reduce the coefficient search space and the associatedcomputations. The embodiment diagrammed in FIG. 8 selects thecoefficients based solely on the coefficient amplitude and can beexpected to require the least amount of computation and be the simplestto implement.

The embodiment of FIG. 6 is useful to illustrate the fundamental conceptof the coefficient selection process 182 which is to eliminate computedcoefficients so that the sparse time domain filters can be used in theDFE with either a DFE performance improvement or an insignificantperformance loss. However, the embodiment of FIG. 6 is anticipated toexhibit an excessive computational demand. On the other hand,embodiments of FIGS. 7 and 8 are practical implementations that havebeen extensively tested by means of computer simulation using acceptedWMAN CIR models. Some of these simulation results are described inRussell McKown, “802.16e Proposal: Link Performance of WirelessMAN-SCaMobile Subscriber Stations”, IEEE c802.16e-03/19r2, Mar. 11, 2003, whichis incorporated herein by reference.

What is claimed is:
 1. An method, comprising: estimating a channelimpulse response; determining feed forward coefficients and feedbackcoefficients for at least one time domain filter based on the channelimpulse response; and selecting a subset of the feed forwardcoefficients and a subset of the feedback coefficients wherein a numberof coefficients in each subset is less than a total number of thedetermined coefficients.
 2. The method of claim 1, wherein selecting asubset of feed forward coefficients and a subset of the feedbackcoefficients comprises: selecting a coefficient having an amplitudebeing one of a largest coefficient amplitudes of the feed forwardcoefficients or the feedback coefficients.
 3. The method of claim 2,wherein selecting a subset of feed forward coefficients and a subset ofthe feedback coefficients further comprises: selecting a coefficienthaving an amplitude greater than K*.sigma..sub.F or K*.sigma..sub.B,wherein sigma..sub.F and .sigma..sub.B are standard deviations of asubset of coefficients whose amplitudes are not one of the largestcoefficient amplitudes of the feed forward coefficients or the feedbackcoefficients, wherein K is a threshold parameter that providesprotection against coefficient computation noise.
 4. The method of claim3, wherein the selecting a subset of the feed forward coefficients and asubset of the feedback coefficients comprises: pre-selecting computedfeed forward coefficients and feedback coefficients.
 5. The method ofclaim 4, wherein the pre-selecting the computed feed forwardcoefficients and feedback coefficients comprises: examining the computedfeed forward coefficients and feedback coefficients; and storing each ofthe computed coefficients having an amplitude being one of a largestcoefficient amplitudes in a coefficient buffer that defines acoefficient search space for a minimization process.
 6. The method ofclaim 4, wherein selecting a coefficient having an amplitude greaterthan K*.sigma..sub.F or K*.sigma..sub.B comprises: sorting the computedfeed forward coefficients into a number of largest feed forwardcoefficients and a number of smallest feed forward coefficients; sortingthe computed feedback coefficients into a number of largest feedbackcoefficients and a number of smallest feedback coefficients; andcalculating sigma..sub.F and sigma..sub.B based on the number ofsmallest feed forward coefficients and the number of smallest feedbackcoefficients.
 7. The method of claim 6, further comprising: selecting acoefficient to include in the subset of feed forward coefficients if theamplitude of the coefficient is one of a largest coefficient amplitudesof the feed forward coefficients and is greater than K*.sigma..sub.F;and selecting a coefficient to include in the subset of feedbackcoefficients if the amplitude of the coefficient is one of a largestcoefficient amplitudes of the feedback coefficients and is greater thanK*.sigma..sub.B.
 8. An apparatus, comprising: circuitry for estimating achannel impulse response; circuitry for determining feed forwardcoefficients and feedback coefficients; and circuitry for selecting asubset of the feed forward coefficients and a subset of the feedbackcoefficients, wherein a number of coefficients in each subset is lessthan a total number of the determined coefficients.
 9. The apparatus ofclaim 8, wherein the circuitry for selecting a subset of the feedforward coefficients and a subset of the feedback coefficientscomprises: circuitry for selecting each coefficient in the subsets ofthe coefficients based on an amplitude of the coefficient satisfying atleast one of: the amplitude being one of a largest coefficientamplitudes of the feed forward coefficients or the feedbackcoefficients; and the amplitude being greater than K*.sigma..sub.F orK*.sigma..sub.B, where sigma..sub.F or sigma..sub.B are standarddeviations of a subset of coefficients whose amplitudes are not one ofthe largest coefficient amplitudes of the feed forward coefficients orthe feedback coefficients, wherein K is a threshold parameter thatprovides protection against coefficient computation noise.
 10. Theapparatus of claim 8, wherein the circuitry for selecting a subset ofthe feed forward coefficients and a subset of the feedback coefficientscomprises: circuitry for pre-selecting the feed forward coefficients andfeedback coefficients.
 11. The apparatus of claim 10, wherein thecircuitry for pre-selecting the feed forward coefficients and feedbackcoefficients comprises: circuitry for examining the determined feedforward coefficients and feedback coefficients; circuitry for selectinga coefficient having an amplitude being one of a largest coefficientamplitudes from the determined feed forward coefficients and feedbackcoefficients; and circuitry for storing the coefficient having anamplitude being one of a largest coefficient amplitudes in a coefficientbuffer that defines a coefficient search space for a minimizationprocess.
 12. The apparatus of claim 9, wherein the circuitry forselecting a subset of the feed forward coefficients and a subset of thefeedback coefficients comprises: circuitry for sorting the determinedfeed forward coefficients into a number of largest feed forwardcoefficients and a number of smallest feed forward coefficients; andcircuitry for calculating the sigma..sub.F based on the number ofsmallest feed forward coefficient.
 13. The apparatus of claim 9, whereinthe circuitry for selecting a subset of the feed forward coefficientsand a subset of the feedback coefficients comprises: circuitry forsorting the determined computed feedback coefficients into a number oflargest feedback coefficients and a number of smallest feedbackcoefficients; and circuitry for calculating the sigma..sub.B based onthe number of smallest feedback coefficients.
 14. The apparatus of claim12, wherein the circuitry for selecting a subset of the feed forwardcoefficients and a subset of the feedback coefficients furthercomprises: circuitry for selecting a coefficient to include in thesubset of feed forward coefficients if the amplitude of coefficient isone of a largest coefficient amplitudes of the feed forward coefficientsand is greater than K*.sigma..sub.F.
 15. The apparatus of claim 13,wherein the circuitry for selecting a subset of the feed forwardcoefficients and a subset of the feedback coefficients furthercomprises: circuitry for selecting a coefficient to include in thesubset of feedback coefficients if the amplitude of the coefficient isone of a largest coefficient amplitudes of the feed forward coefficientsand is greater than K*.sigma..sub.B.
 16. An apparatus, comprising:circuitry for estimating a channel impulse response; circuitry fordetermining feed forward filter coefficients and feedback filtercoefficients for a decision feedback equalizer having sufficient lengthto cover a maximum anticipated channel impulse response; and circuitryfor pre-selecting the feed forward filter coefficients and the feedbackfilter coefficients.
 17. The apparatus of claim 16, wherein thecircuitry for pre-selecting the feed forward filter coefficients andfeedback filter coefficients comprises: circuitry for selecting a numberof largest feed forward coefficients and a number of largest feedbackcoefficients; a buffer for storing the number of largest feed forwardcoefficients and largest feedback coefficients; and circuitry foridentifying from the number of largest feed forward coefficients andlargest feedback coefficients a subset of coefficients.
 18. Anapparatus, comprising: circuitry for estimating a channel impulseresponse; circuitry for determining feed forward filter coefficients andfeedback filter coefficients; circuitry for sorting the feed forwardfilter coefficients and the feedback filter coefficients based onamplitudes of the coefficients; circuitry for computing standarddeviations of the coefficients whose amplitudes are not one of thelargest coefficient amplitudes of the feed forward filter coefficientsor the feedback filter coefficients; and circuitry for selecting asubset of the feed forward coefficients and a subset of the feedbackcoefficients based on the standard deviations.
 19. The apparatus ofclaim 18, wherein the circuitry for sorting the feed forward filtercoefficients and the feedback filter coefficients based on amplitudes ofthe coefficients comprises: circuitry for sorting circuitry for sortingthe determined computed feedback coefficients into a number of largestfeed forward coefficients and a number of smallest feed forwardcoefficients based on the amplitudes.
 20. The apparatus of claim 19,wherein the circuitry for computing standard deviations comprisescircuitry for computing the standard deviations based on the smallestnumber of feed forward coefficients and the smallest number of feedbackcoefficients, and p1 the circuitry for selecting a subset of the feedforward coefficients and a subset of the feedback coefficients comprisesa threshold comparison circuitry for comparing the number of largestfeed forward coefficients and the number of smallest feedbackcoefficients to a product of the standard deviations and a thresholdparameter that provides protection against coefficient computationnoise.